Planar polymers under cylindrical confinement*

We show that the cylindrical confinement of a planar ribbon gives rise to the formation of stationary helical shapes, previously observed in molecular dynamics simulation studies of some planar polymers inside nanotubes. In the limit of small twisting deformations, we notice that a confined ribbon describes identical equilibrium configurations of an elastic rod on the plane. Also, every locally planar strip adsorbed on a cylinder is forced to follow a helical envelope, as its length increases. We also determine the forces and torques that sustain each ribbon equilibrium configuration through the equilibrium geometry and the confinement surface parameters.